To determine how many numbers between 1 and 200 are divisible by 13, we need to find those numbers which, when divided by 13, yield an integer result.
The formula to find the number of integers divisible by a number \(n\) between two numbers \(a\) and \(b\) is:
\(\left\lfloor \frac{b}{n} \right\rfloor - \left\lfloor \frac{a-1}{n} \right\rfloor\)
In this problem, \(n = 13\), \(a = 1\), and \(b = 200\).
Find the largest integer ≤ 200 divisible by 13:
\(\left\lfloor \frac{200}{13} \right\rfloor = \left\lfloor 15.3846 \right\rfloor = 15\)
Find the largest integer < 1 divisible by 13:
\(\left\lfloor \frac{0}{13} \right\rfloor = 0\)
Thus, the count of numbers between 1 and 200 that are divisible by 13 is:
\(15 - 0 = 15\)
Therefore, the correct answer is 15.
This confirms option
15
as the correct answer.